Euler Graphs, Triangle-Free Graphs and Bipartite Graphs in Switching Classes

In the context of graph transformations we look at the operation of switching, which can be viewed as a method for realizing global transformations of graphs through local transformations of the vertices. A switching class is then a set of graphs obtainable from a given start graph by applying the switching operation. Continuing the line of research in Ehrenfeucht, Hage, Harju and Rozenberg we consider the problem of detecting three kinds of graphs in switching classes. For all three we find algorithms running in time polynomial in the number of vertices in the graphs, although switching classes contain exponentially many graphs.